No original copies of New Testament Books exist today. That is, we do not possess any of Paul's original
letters, Matthew's original gospel, or the book of Acts in Luke's handwriting. All we have are copies.
There are several reasons for this:

It is generally acknowledged that all New Testament books
were first written on papyrus, a paper-like product made from plant stems. It was readily available
and quite inexpensive. In fact, it was the writing material of choice in the 1st Century. However,
papyrus disintegrates in the presence of moisture. Even very arid places like the Holy Land are way too wet
for papyrus to have survived 2,000 years. Without a doubt, unless they were saved in a very dry place,
the original papyri have long ago decomposed.

No attempt was ever made to
keep or archive the original writings. Both the authors, and those reading these documents,
expected Christ's soon return —
within their lifetimes. As such, they felt no need to save these writings for posterity.

The Apostles were "living
books", and as long
as they were present, there was no need for written records. In I Cor 15:6 Paul refers to
500 witnesses to Christ after his resurrection, most of whom were still alive. A 2nd Century bishop
named Papias wrote, "I do not think that I derived so much benefit from books as from the living
voice of those that are still surviving."

We wouldn't recognize the
originals, even if we found
them. Scholars would, through careful and extensive examination, be able to date a papyrus writing
to the 1st Century, but we would never know for sure if we had the original, or just an early copy.

If we do not have access to the original writings, how can
we tell when the various books of the New Testament were written? We can do that a couple ways:

By dating manuscripts
based on their characteristics.

Earliest New Testament Papyrus FragmentJohn 18:31-33

There are over 5,000 Greek manuscripts in existence that contain at
least a portion of the New Testament. Currently the earliest fragment of any New Testament book is a small
piece of papyrus found in Egypt containing John 18:31-33 on one side
and John 18:37 on the other. It has been dated
to between 100 AD and 130 AD. Although this fragment is not from the original Gospel of John, it is
sufficiently old to have been copied from the original.

There may be an even earlier example.
Some scholars feel that a codex ("codex" is another name for a book of handwritten pages)
known as Chester Beatty Papyrus II, which contains all of Paul's epistles, was written even earlier —
between 90 AD and 100 AD. They base this estimate on handwriting analysis. Should this date be correct,
then we have an entire collection of Paul's Epistles compiled less than 40 years after Paul
originally wrote them.

For the record, other scholars date this same papyrus to around 200 AD. But they base that
belief not on the handwriting, but on the fact that they simply cannot believe that all of Paul's letters
could have been compiled together into a single book before the Year 200.
This shows how pre-conceived ideas can affect textual evaluation. It also shows that the
dating of ancient manuscripts is far from an exact science.

It must be remembered when looking at these dates that there were no means of general publishing
and distribution of books at the time. If we say the Gospel of Mark was written around 65 AD,
that means a single copy of this work — the original — existed in that year. By the end of the
1st Century, there were many active Christian churches in dozens of countries. It would take
decades for original New Testament works to be copied, transported to churches in
Asia, Africa and Europe, and be accepted there as Scripture. So when we find a fragment of John's
gospel in Egypt that dates to between 100 AD and 130 AD, this tends to authenticate the fact that
this book existed at least 25 to 40 years earlier; it would have taken that long for the Gospel
to have reached Egypt and be circulated to the churches there.

We date books by looking for Bible quotations
in documents we can date.Enter the writings of the leaders
of the early church — also referred to as the Apostolic or Church Fathers. These people
wrote between 90 AD and 160 AD. The history of their lives is fairly well documented, so it is
easier to date their writings.

In three works that date around 100 AD — "The Epistle of Barnabus",
"The Teaching of the Twelve Apostles",
and "I Clement" — there are fairly certain quotations from
the Gospels, Acts, Romans, I Corinthians, Ephesians, Titus, Hebrews, and I Peter.
Ignatius was
Pastor of the church at Antioch; he died a martyr's death in 115 AD. From his letters we find
passages from Matthew, John, Romans, I & II Corinthians, Galatians, Ephesians, Philippians,
I & II Timothy, and Titus. Polycarp, another early church leader,
wrote a letter to the Philippian Church in 120 AD. In it he quotes from more than half the books
in the New Testament. Here are some other examples:

CHURCH FATHERS

NEW TESTAMENT

By him would God have us to taste the knowledge of
Immortality: who being the brightness of his glory, is by so much greater than the angels, as he
has by inheritance obtained a more excellent name than they.[I Clement 17:18]

Who being the brightness of his glory, and the
express image of his person ... sat down on the right hand of the Majesty on high; being made so
much better than the angels and he hath by inheritance obtained a more excellent name than they.
[Hebrews 1:3,4]

Let us then not only call him Lord; for that
will not save us. For he saith: Not every one that saith unto me Lord, Lord, shall be saved, but
he that doeth righteousness.
[II Clement 2:12]

Not every one that saith unto me, Lord, Lord,
shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
[Matthew 7:21]

It is therefore fitting that you should by all
means glorify Jesus Christ who hath glorified you: that by a uniform obedience ye may be perfectly
joined together, in the same mind, and in the same judgment: and may all speak the same things
concerning everything.
[Ignatius to the Ephesians 1:8]

Now I beseech you, brethern, by the name of
our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you:
but that ye be perfectly joined together in the same mind and in the same judgment.
[I Corinthians 1:10]

But remembering what the Lord has taught us
saying, Judge not, and ye shall not be judged; forgive, and ye shall be forgiven; be ye
merciful, and ye shall obtain mercy; for with the same measure that ye mete withal, it shall
be measured to you again.
[Polycarp to the Philippians 1:10]

Judge not, and ye shall not be judged: condemn
not, and ye shall not be condemned: forgive, and ye shall be forgiven. ... For with the same
measure that ye mete withal, it shall be measured to you again.
[Luke 6:37,38]

Although information like this does not specifically date various
books, it does establish that latest date when these writings could have been created.

Up until recently there was a widespread school of thought that considered most New Testament
books to have been written around 150 AD. This, of course, would preclude their authorship by the men
we traditionally credit with their writing. However, discoveries in the past 50 years — both
archeologically and textually — have brought to light information that tends to verify the
belief that most New Testament books were written within 40 years of Christ's
ascension, and that the entire New Testament was complete by 100 AD.

The dates below came from F. F. Bruce, who was a well-respected Bible scholar.

MATTHEW:

Shortly after 70 AD

MARK:

64 to 65 AD

LUKE:

Shortly before 62 AD (perhaps later)

JOHN:

90 to 100 AD

ACTS:

65 AD (perhaps later)

ROMANS:

57 AD (perhaps later)

I & II CORINTHIANS:

54 to 56 AD

GALATIANS:

48 AD

EPHESIANS:

60 AD

PHILIPPIANS:

60 AD

COLOSIANS:

60 AD

I & II THESSALONIANS:

50 AD

PHILEMON:

60 AD

REVELATION:

90 to 100 AD

There are even a few historians who present good arguments
that the entire New Testament was complete shortly before the destruction of Jerusalem in 70 AD. But
for me, I'll stick with F. F. Bruce's dates above.